(b-4)(b-6)=80

Solution for (b-4)(b-6)=80 equation:

Simplifying
(b + -4)(b + -6) = 80

Reorder the terms:
(-4 + b)(b + -6) = 80

Reorder the terms:
(-4 + b)(-6 + b) = 80

Multiply (-4 + b) * (-6 + b)
(-4(-6 + b) + b(-6 + b)) = 80
((-6 * -4 + b * -4) + b(-6 + b)) = 80
((24 + -4b) + b(-6 + b)) = 80
(24 + -4b + (-6 * b + b * b)) = 80
(24 + -4b + (-6b + b2)) = 80

Combine like terms: -4b + -6b = -10b
(24 + -10b + b2) = 80

Solving
24 + -10b + b2 = 80

Solving for variable 'b'.

Reorder the terms:
24 + -80 + -10b + b2 = 80 + -80

Combine like terms: 24 + -80 = -56
-56 + -10b + b2 = 80 + -80

Combine like terms: 80 + -80 = 0
-56 + -10b + b2 = 0

Factor a trinomial.
(-4 + -1b)(14 + -1b) = 0

Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve:

Simplifying
-4 + -1b = 0

Solving
-4 + -1b = 0

Move all terms containing b to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1b = 0 + 4
-1b = 0 + 4

Combine like terms: 0 + 4 = 4
-1b = 4

Divide each side by '-1'.
b = -4

Simplifying
b = -4
Subproblem 2
Set the factor '(14 + -1b)' equal to zero and attempt to solve:

Simplifying
14 + -1b = 0

Solving
14 + -1b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-14' to each side of the equation.
14 + -14 + -1b = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1b = 0 + -14
-1b = 0 + -14

Combine like terms: 0 + -14 = -14
-1b = -14

Divide each side by '-1'.
b = 14

Simplifying
b = 14
Solution
b = {-4, 14}